There are many points of comparison between these two presidents. Perhaps the one that offers the clearest contrast between the two is the area of foreign policy.

In foreign policy, Roosevelt was avowedly looking out for the interests of the United States. He was not trying to be idealistic or spread democracy or anything like that. He practiced his "big stick" diplomacy, throwing the US's weight and power around to get things that he felt would help the US (like the Panama Canal Zone).

By contrast, Wilson tended to try to be idealistic. For example, he took actions in Mexico that (you can argue) were against US interests. He chose what he saw as a democratically elected leader over one who would be more friendly to the US. When WWI came around, he tried to broker a peace based on ideals rather than on power. In these ways, he was clearly trying to be idealistic.